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GAIA Seminar on Complex Analytic Geometry- Sungmin Yoo

posted Sep 29, 2014, 1:19 AM by Inyoung Park

Title: Representative maps and connections.

Speaker:Sungmin Yoo (POSTECH)

Abstract: The Bergman kernel function gives rise not only to the Bergman metric but also to some special holomorphic coordinate system which is called the Bergman representative map. This map appears to be quite similar to inverse of exponential map of Riemannian geometry. In this talk, I would demonstrate a construction of a holomorphic connection on the holomorphic tangent bundle of a subdomain of a given complex manifold, whose parallel curve gives rise to the inverse of the Bergman representative map. This overlaps largely to the work of S. Webster. I will also discuss some further results if time permits.